Thomas Hasanis, Rafael López
Abstract
We prove that the only surfaces in $3$-dimensional Euclidean space $\R^3$ with constant Gaussian curvature $K$ and constructed by the sum of two space curves are cylindrical surfaces, in particular, $K=0$.
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We prove that the only surfaces in $3$-dimensional Euclidean space $\R^3$ with constant Gaussian curvature $K$ and constructed by the sum of two space curves are cylindrical surfaces, in particular, $K=0$.
Key concepts: Gaussian curvature, Mathematics, Translation (biology), Euclidean space, Constant (computer programming), Space (punctuation), Euclidean geometry, Constant curvature